Chapter 7 - Circular Motion and Gravitation - Learning Path Questions and Exercises - Exercises - Page 262: 46

a). $-78.5rad/s^{2}$ b). $2s$

a). Initial angular velocity =$25 rev/s=25\times2pi \,\,\,\,rad/s=157rad/s$ $\Delta\theta=50 rev=50\times2pi \,\,rad=157rad$ From equation, $\omega^{2}=\omega_{0}^{2}+2a\Delta\theta$, $0=\omega_{0}^{2}+2a\Delta\theta$ $a=-\frac{\omega_{0}^{2}}{2\Delta\theta}=-78.5rad/s^{2}$ b). $t=\frac{\omega-\omega_{0}}{a}=\frac{0-157}{-78.5}=2s$